On Motion and Impact: Descending a Staircase in Leaps
The summed impacts of jumping step by step equal one perpendicular fall from top to bottom
Written upside-down on the leaf, this note 'On motion and impact' argues that if a man descends a staircase leaping from step to step, the summed powers and weights of all those impacts equal the single impact and weight he would deliver by falling straight down the whole height of the stair. Leonardo adds that if he fell striking successive objects that yield like springs, so that each impact is small, his final impact would be reduced below that of a free perpendicular fall by exactly the sum of the impacts absorbed along the way. The page is entirely text, with no diagram.
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Summed impacts of a stepwise descent equal one perpendicular fall
Descending step by step with a jump between each, the total of all the powers of the impacts and the weights of the jumps is equal to the whole impact and weight the man would deliver falling in a single perpendicular line down the full height of the stair.
Spring-like steps diminish the final impact
If the man fell striking objects that yield like a spring, so each impact is small, his impact at the end of the descent would be less than that of a free perpendicular fall by exactly the sum of all the impacts absorbed at each degree along the way.